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l-1j-cho
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how do you prove, if p is prime, then a derived equation of p is prime, if true?
You can't be saying "if p is prime, (2^p - 1) is prime" because that is not true for p = 11. But it is easy to show that (2^p -1) can be prime only if p is prime. As for equations being prime, do you mean proving that a polynominal is not factorable into the product of two polynominals of lower degree? Or do you mean to show that a certain polynomial in n yields primes for all positive values of n less than a certain integer?l-1j-cho said:hello!
uhm, I don't know anything in particular, but something like
if p is prime, the following equation is prime
or if p is prime, (2^p -1) is prime such things
It has been proven that such polynominals don't exist since if P(n) is prime then P(n+a*prime) is also divisible by "prime",l-1j-cho said:oh right my apology
I mean polynomials that is expressed in terms of p.
obviously, polynomials like p^2+5p+6 is not prime because if can be factored to (p+2)(p+3)
but my question is, how do you prove that a random polynomials always spits out a prime number whenever we plug in a prime number?
but before that, would such polynomial exist?
(not necesarrily polynomials but exponents or other stuff)
ramsey2879 said:P(n+a*prime) is also divisible by prime,
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sorry but, could you explain about this more?
ramsey2879 said:It has been proven that such polynominals don't exist since if P(n) is prime then P(n+a*prime) is also divisible by "prime",
. Don't know but very much doubt that there is some exotic function in P that is prime for all prime P.
l-1j-cho said:ramsey2879 said:P(n+a*prime) is also divisible by prime,
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sorry but, could you explain about this more?
Sure 3p +2 = 23 for p = 7, so for p = 7 + a*23 e.g. for p = 7,30,53,... ,3p + 2 is divisible by 23 and hence not prime. The same goes for any polynominal in p.
A prime number is a positive integer that is only divisible by 1 and itself.
One way to prove that a number is prime is by using the Sieve of Eratosthenes, which involves eliminating all multiples of a number until only the initial number remains.
As of 2021, the largest known prime number is 2^(82,589,933) − 1, which has over 24 million digits.
No, there are some numbers that are considered "probable primes" because they have not been proven to be either prime or composite using current methods. However, they are still treated as prime numbers in many applications.
Proving prime numbers is important in cryptography and computer science, as well as in pure mathematics. It helps us to understand the properties of numbers and can be used in various mathematical algorithms and applications.